It is known in displacement measuring apparatus, e.g. for machine tools, to provide a mark-space grid on one of two relatively movable members and a reading head on the other of said members. The reading head is connected to a control unit situated on the one member, the latter usually being stationary, by a flexible cable for two-way transmission of electrical signals. Further, the reading head includes an optoelectronic system for converting an electrical signal received from the control unit into an optical signal for illumination of the grid, and for converting optical signals generated by the marks and spaces of the grid into electrical signals for transmission to the control unit, there to be converted into actual dimensions of measurement. Also, the head usually embodies means for determining the sense of direction of the movement. It has been found that the reading head can be relatively bulky or sensitive to vibration, or that the apparatus can be needful of relatively expensive connector and cable means for transmission of the electrical signal between the head and the control unit. It is generally an object of this invention to overcome or reduce those difficulties.